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Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: Sequential sampling and optimization on the potential of mean force surface
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10.1063/1.2816557
/content/aip/journal/jcp/128/3/10.1063/1.2816557
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/3/10.1063/1.2816557

Figures

Image of FIG. 1.
FIG. 1.

Path optimization scheme and different choices for the reference QM conformations in the PMF and PMF gradient calculations of the QM/MM-MFEP method.

Image of FIG. 2.
FIG. 2.

Second proton transfer step of the reaction catalyzed by the enzyme 4-OT.

Image of FIG. 3.
FIG. 3.

Reaction free energies for in solution simulated by umbrella sampling and WHAM analysis. The QM methods used were: MP2/6- (dot-dash), MP2/6- (dash), B3LYP/6- (solid), and B3LYP/6- (dot).

Image of FIG. 4.
FIG. 4.

Reaction free energies for in solution simulated with QM/MM-MFEP and QSM. (a) Direct QSM optimization with the structures of the reactant and product state frozen; (b) two separate QSM simulations connecting the reactant state with the transition state, and the transition state with the product state.

Image of FIG. 5.
FIG. 5.

Solution-phase stationary point structures of the complex optimized by the QM/MM-MFEP method: (a) reactant (and product) state; (b) transition state.

Image of FIG. 6.
FIG. 6.

Stationary point structures from the active site of 4OT optimized with the QM/MM-MFEP method: (a) reactant state; (b) transition state; and (c) product state.

Image of FIG. 7.
FIG. 7.

Reaction free energies of the second proton transfer step of the reaction catalyzed by 4OT using QM/MM-MFEP and QSM.

Image of FIG. 8.
FIG. 8.

Convergence of the QM/MM-MFEP and QSM optimizations for the 4OT and reactions. (a) Convergence of the relative free energies in the optimization of the reactant state of 4OT. Each vertical line indicates the start of a new cycle. The -axis is the accumulated number of QM steps made by the QM optimization algorithm. Vertical lines indicate the onset of a new cycle of sequential MM sampling and QM optimization. The number of vertical lines is the number of times MM ensembles are generated. (b) Convergence of the norm of the gradient for one conformational state on the path of the 4OT reaction. (c) Evolution of the PMF profiles during successive cycles of QSM optimization of the 4OT reaction: cycle 1 (blue), cycle 2 (green), cycle 3 (red), cycle 4 (black). (d) Convergence of the relative free energies in the optimization of the reactant state for the reaction. Each vertical line indicates the start of a new cycle.

Image of FIG. 9.
FIG. 9.

Correlation between the free-energy gradient computed using analytical and numerical approaches. The -axis contains the numerical free-energy gradient computed for the complex in solution, and the -axis contains the free-energy gradient computed with the analytical equations described in Sec. II, Theory.

Tables

Generic image for table
Table I.

Vibrational frequencies (in ) of the transition state (TS) and reactant state (RS) of the complex in solution.

Generic image for table
Table II.

Geometric measurements of the reactant state (RS), product state (PS), and transition state (TS) for the reaction . Bond lengths are in , and bond angles are in degrees.

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/content/aip/journal/jcp/128/3/10.1063/1.2816557
2008-01-16
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: Sequential sampling and optimization on the potential of mean force surface
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/3/10.1063/1.2816557
10.1063/1.2816557
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